Verification of Time Ontologies with Points and Intervals

Ontology verification is concerned with the relationship between the intended structures for an ontology and the models of the axiomatization of the ontology. The verification of a particular ontology requires characterization of the models of the ontology up to isomorphism and a proof that these models are equivalent to the intended structures for the ontology. In this paper we consider the verification of three time ontologies (first introduced by Hayes in his Catalog of Temporal Theories) that axiomatize both time points and time intervals together with the relationships between them. We identify axioms that are missing from these ontologies and provide a complete account of the metatheoretic relationships between the ontologies.